Learning a Reactive Potential for Silica-Water Through Uncertainty Attribution

Abstract

Silica has various polymorphs with different properties, leading to its application in various industries including windowpanes, catalysts, aerogels, rubber and plastic. Despite much progress involving atomistic simulations of different forms of silica, small amorphous silica clusters are still a challenge. Quantum mechanical (QM) calculations have been employed to study the stability of silicate clusters but are limited to a few atoms, often extrapolating to trimers only and cannot deal with reactions involving silicate polymerization in water solvent under different environmental conditions of different temperatures, pH of solutions and different concentration ratio of reactants. Classical reactive force fields can scale up to a large number of atoms but lack in accuracy compared to first principle calculations. Recently, the advent of machine-learning models in materials science has enabled replicating QM accuracy with time and length scale compared to empirical potentials. Neural network-based interatomic potentials (NNIPs) on condensed phase silica and porous crystalline zeolites trained on QM data have proved to be more accurate than classical potentials and have opened doors to large-scale simulations with high-level QM accuracy. We aim to train a reactive NNIP for silicate polymerization reactions in a water solvent. These reactions are significant to understand the formation of precipitated silica as well as the preliminary stage in zeolite crystallization. Our NNIP is based on a rotationally equivariant message passing neural network known as polarizable atom interaction neural network (PAiNN). Our current dataset comprises 210K molecular clusters with forces and energies calculated using a long-range corrected hybrid functional ωB97XD3. Despite training on molecular clusters, we can perform periodic molecular dynamics (MD) simulations and predict the properties of condensed phases. Hereon, we also propose a new active learning method based on per-atom attribution of model uncertainty to enlarge our dataset with robust and diverse set of molecular configurations. With this method, we can quantitatively identify inter-atomic interactions with high inaccuracy; carve out an atomic environment within a cut-off on which the potential performs poorly, and thus save QM calculation cost. The method involves taking the derivative of the uncertainty of NNIP ensemble with respect to atomic positions and marks highly uncertain inter-atomic interactions. We then select a molecular cluster environment with a high attributed atom at its center for QM calculations and add to training data. Upon running this automated active learning loop for a few generations, we visualize consecutive improvement of attributions on atoms and thus proving the efficiency of this proposed method. The current NNIP after eight generations of active learning is successful to predict the properties of liquid water as well as reactions involving deprotonation of water and silicate dimerization in a dilute water solvent. The radial density functions (RDFs) of O-O, O-H and H-H in water obtained from molecular dynamics simulations using our NNIP are comparable to experimental and reported results. The self-diffusivity of water at 300K is predicted as 2.26+-0.06 x $ 10^{-9} m^2/s $ , close to the experimental one (2.41 x $ 10^{-9} m^2/s $ ) and the density is predicted as 1.08g/cc. The reaction involving deprotonation of water molecule is replicated accurately with enhanced sampling based MD and the $ pK_w $ of water is predicted as 17.4, which is close to expected value of 17 (higher than experimental due to quantum nuclear effect). The NNIP further predicts the relative energy of siliceous zeolites with respect to quartz with error of only 1.2 KJ/mol compared to experimental results. This robust NNIP can replicate the reaction path of silicate dimerization and will be further used to replicate deprotonation of orthosilicic acid and then silicate condensation and hydrolysis reactions.